The Theory of Finite Groups

The Theory of Finite Groups
Author: Hans Kurzweil
Publisher: Springer Science & Business Media
Total Pages: 390
Release: 2006-03-04
Genre: Mathematics
ISBN: 0387217681

From reviews of the German edition: "This is an exciting text and a refreshing contribution to an area in which challenges continue to flourish and to captivate the viewer. Even though representation theory and constructions of simple groups have been omitted, the text serves as a springboard for deeper study in many directions." Mathematical Reviews

Finite and Locally Finite Groups

Finite and Locally Finite Groups
Author: B. Hartley
Publisher: Springer Science & Business Media
Total Pages: 469
Release: 2012-12-06
Genre: Mathematics
ISBN: 9401103291

This volume contains the proceedings of the NATO Advanced Study Institute on Finite and Locally Finite Groups held in Istanbul, Turkey, 14-27 August 1994, at which there were about 90 participants from some 16 different countries. The ASI received generous financial support from the Scientific Affairs Division of NATO. INTRODUCTION A locally finite group is a group in which every finite set of elements is contained in a finite subgroup. The study of locally finite groups began with Schur's result that a periodic linear group is, in fact, locally finite. The simple locally finite groups are of particular interest. In view of the classification of the finite simple groups and advances in representation theory, it is natural to pursue classification theorems for simple locally finite groups. This was one of the central themes of the Istanbul conference and significant progress is reported herein. The theory of simple locally finite groups intersects many areas of group theory and representation theory, so this served as a focus for several articles in the volume. Every simple locally finite group has what is known as a Kegel cover. This is a collection of pairs {(G , Ni) liE I}, where I is an index set, each group Gi is finite, i Ni

Finite Groups

Finite Groups
Author: Daniel Gorenstein
Publisher: American Mathematical Soc.
Total Pages: 546
Release: 2007
Genre: Mathematics
ISBN: 0821843427

"The Classification Theorem is one of the main achievements of 20th century mathematics, but its proof has not yet been completely extricated from the journal literature in which it first appeared. This is the second volume in a series devoted to the presentation of a reorganized and simplified proof of the classification of the finite simple groups. The authors present (with either proof or reference to a proof) those theorems of abstract finite group theory, which are fundamental to the analysis in later volumes in the series. This volume provides a relatively concise and readable access to the key ideas and theorems underlying the study of finite simple groups and their important subgroups. The sections on semisimple subgroups and subgroups of parabolic type give detailed treatments of these important subgroups, including some results not available until now or available only in journal literature. The signalizer section provides an extensive development of both the Bender Method and the Signalizer Functor Method, which play a central role in the proof of the Classification Theorem. This book would be a valuable companion text for a graduate group theory course."--Publisher's website

Groups St Andrews 2009 in Bath: Volume 2

Groups St Andrews 2009 in Bath: Volume 2
Author: C. M. Campbell
Publisher: Cambridge University Press
Total Pages: 305
Release: 2011-06-16
Genre: Mathematics
ISBN: 1139498282

This second volume of a two-volume book contains selected papers from the international conference Groups St Andrews 2009. Leading researchers in their respective areas, including Eammon O'Brien, Mark Sapir and Dan Segal, survey the latest developments in algebra.

P-Automorphisms of Finite P-Groups

P-Automorphisms of Finite P-Groups
Author: Evgenii I. Khukhro
Publisher: Cambridge University Press
Total Pages: 226
Release: 1998-02-13
Genre: Mathematics
ISBN: 052159717X

Ideal for graduate students and researchers working in group theory and Lie rings.

Nilpotent Groups and their Automorphisms

Nilpotent Groups and their Automorphisms
Author: Evgenii I. Khukhro
Publisher: Walter de Gruyter
Total Pages: 269
Release: 2011-04-20
Genre: Mathematics
ISBN: 3110846217

The aim of the series is to present new and important developments in pure and applied mathematics. Well established in the community over two decades, it offers a large library of mathematics including several important classics. The volumes supply thorough and detailed expositions of the methods and ideas essential to the topics in question. In addition, they convey their relationships to other parts of mathematics. The series is addressed to advanced readers wishing to thoroughly study the topic. Editorial Board Lev Birbrair, Universidade Federal do CearĂ¡, Fortaleza, Brasil Victor P. Maslov, Russian Academy of Sciences, Moscow, Russia Walter D. Neumann, Columbia University, New York, USA Markus J. Pflaum, University of Colorado, Boulder, USA Dierk Schleicher, Jacobs University, Bremen, Germany